I am the same position; the LK is showing warning but still prints.
On LK, I can understand that this provides a neutral grey base for many non saturated areas. My LK however, was at 20% (while others all were at 50%) right after the initial charging. I wonder why this is? Are there more tubes for LK? does the charging involve dumping of colors?
The LK ink shares a channel with the PK/MK inks. When charging the printer, it will first push through LK and MK. Once the MK is charged, it will switch to PK in the head, but then has to charge the full PK line. When doing this it basically charges the LK line a second time. So once the printer is primed, it will have about 60% remaining in all of the colors but LK, where it will be down to about 38%.
Additionally, anytime you switch from PK to MK it will consume some LK ink as well.
The high usage of LK ink makes it is the most critical and by far the highest consumed ink, so the quickly consumed LK ink is quite conspicuous.. I was sort of wondering if the startup procedure could have you leave the LK cartridge out until the MK line is charged so it's just pumping air. Maybe that messes up the pump if it's running "dry" like that. Also thought it would be nice if MK/PK shared a channel with a very low consumption color. (Idle curiosity here - I'm certainly not an engineer and by all mean's it's not a big deal)
I am only running 350ml cartridges in my printer, but I've decided to use the 700ml for the LK. I'm guessing it will still run out before the other colors. Not complaining, just an observation. This is all ink that's going on a piece of paper (when needing MK I use my 11880).
Anyway, for anyone buying one of these printers, I recommend you purchase a spare LK cartridge with the printer, because even with color printing LK ink is consumed at 3 to 6 times faster than any other color.